MATH 4547/6547– Learning Outcomes
Title: Introduction to Statistical Methods
- Students will understand graphical methods of describing data sets and be able to calculate and interpret numerical descriptive statistical measures.
- Students will understand basic probability theory, including rules for finding probabilities of complex events, conditional probability, and probabilities for repeated independent and dependent trials.
- Students will understand the concepts of sampling, including the use of random number tables to select samples.
- Students will understand the probability distributions of discrete random variables, including calculation of means and variances of such distributions.
- Students will understand the binomial probability distribution, including calculation of probabilities, means, and variances.
- Students will understand the use of density functions to describe distributions of continuous random variables.
- Students will be able to calculate probabilities and percentiles for random variables with uniform and normal probability distributions.
- Students will be able to use the normal distribution to approximate binomial probabilities.
- Students will understand the concept of sampling distribution of a statistic and be able to calculate the sampling distribution for simple sampling situations.
- Students will understand the Central Limit Theorem and be able to use it to find probabilities for sample statistics.
- Students will be able to use confidence intervals to estimate unknown population means using large or small samples (with z- or t-distributions) for numerical variables and to estimate unknown proportions in populations for categorical variables.
- Students will understand the concept tests of hypotheses and be able to perform hypothesis tests for means and proportions for one-sample data.
- Students will be able to extend confidence intervals and tests of hypotheses to two-sample situations, including differences in means and proportions for independent samples and differences in means for paired data.
- Students will understand the multinominal probability model and will be able test hypotheses for categorical data in one-way and two-way tables using chi-squared methods.
- Students will be able use the SAS computer software system for basic statistical calculations and basic inferential procedures.
Assessment of Learning Outcomes
Problems based on the learning outcome objectives will be assigned on a regular basis and may appear in a variety of contexts
- Homework problems serve as both learning and assessment tools for both familiarization with and understanding of the topics covered. Evaluation of homework may include grading of assignments or quizzes covering homework assignments.
- Classroom discussion of homework problems and other topics provides additional assessment of students’ understanding of the topics covered.
- Questions in class are used to assess the students’ understanding of concepts covered.
- Computer assignments will be used to evaluate the students’ ability to use the SAS computer software system.
- Midterm and final examinations will be used to evaluate the students’ mastery of the topics covered.